Question: Which of the following numbers is a multiple of 8? ${46,77,89,96,117}$
Solution: The multiples of $8$ are $8$ $16$ $24$ $32$ ..... In general, any number that leaves no remainder when divided by $8$ is considered a multiple of $8$ We can start by dividing each of our answer choices by $8$ $46 \div 8 = 5\text{ R }6$ $77 \div 8 = 9\text{ R }5$ $89 \div 8 = 11\text{ R }1$ $96 \div 8 = 12$ $117 \div 8 = 14\text{ R }5$ The only answer choice that leaves no remainder after the division is $96$ $ 12$ $8$ $96$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $8$ are contained within the prime factors of $96$ $96 = 2\times2\times2\times2\times2\times3 8 = 2\times2\times2$ Therefore the only multiple of $8$ out of our choices is $96$. We can say that $96$ is divisible by $8$.